OK let’s try it this way: Suppose you encountered an economist who argued like this:

[HYPOTHETICAL ECONOMIST HOLDING A STRANGE VIEW:] In a market economy, in competitive equilibrium wages are equal to the marginal product of capital. I can prove this to you mathematically in a simple model where physical machines can do all the jobs that humans can do, and so in equilibrium it must be the case that an hour of labor earns the exact same amount as an hour of machine-time. Moving beyond my formal model where I can literally prove it mathematically, intuitively we can see that wages are determined by the marginal productivity of capital because workers can produce more stuff with an additional unit of capital.

Now, I hope we can all agree that the above is utterly confused. But imagine that you met PhD economists who believed it quite passionately, and indeed there was a bestselling book on Amazon founded on the above framework.

I am being dead serious. Please take this thought experiment seriously, and tell me exactly how you would try to get the above economist to realize his whole framework was messed up, and he needed to not simply tweak it, but to jettison it entirely.

Are you asking whether the equilibrium wage would equal MPC or whether MPC would determine wages, per your original post? They are two different things. Maybe the answer is the same, but I haven’t thought it through yet…

Actually Silas I have that trump card in my back pocket. I can always “demonstrate” that wages are the return on human capital. The marginal productivity of labor thus determines the rate of interest. Or, the marginal productivity of capital determines the wage rate.

Then I’m not sure I follow — isn’t this “obviously absurd” argument (the one you presented as a hypothetical) actually defensible?

Whatever my tone/approach/whatever, I wouldn’t say that such a model is wrong or unrealistic or non-physical. I’d just say that it blurs together two classes of goods whose differences are usually relevant in the contexts where we want to apply the model.

Gah!! The point of my reductio ad absurdum was to get people to realize their arguments trying to defend “interest = MPK” would also lead them to defend “wages = MPK” and thus they would DROP the former. I didn’t want them to embrace the latter!

Here are my thoughts, I am not sure how much sense this makes, but here you go:

I guess he is saying that assuming a lawnmower-bot and a gardener with a lawnmower can give the consumer the same amount of utility for cutting his lawn, then the consumer would be willing to pay the same price for each service.

Now how does this imply that “equilibrium wages are equal to the marginal product of capital?” Say the “marginal product of capital” instead was lower than wages. Then how does this system move back into equilibrium? Do human actors buy more labor and sell more capital until they are in equilibrium again? But if capital already exists, why would one sell it just to make the marginal product of capital equal to wages again? Just because the “marginal product of capital” is less than wages, doesn’t make the capital worthless…

If wages were instead lower than the marginal product of capital, I suppose human actors may rent more capital to expand (or replace the labor.)

Also, as a lawnmower-bot is used more and more, its marginal product of capital may go down as it needs repairs. If a rational human actor does something other than destroy it, and obsolete capital accumulates, the marginal product of capital will go down (I guess same for laborers getting old…)

No philosophically astute person will be persuaded by mere evidence alone; he must have his worldview changed. I believe he needs to be shown: wages paid are subjective to the payor; and, inputs to his mathematical formula will require him to use at least one assumption, which will be based on his conclusion. Thus, he needs to be shown he’s committing the logical fallacy of ‘question begging.’ His worldview is not logically consistent.